This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

An excellent reputation earned by initiating and practicing sustainable business practices has additional benefits, of which are reducing environmental incidents and an improvement in operational efficiency as this has the potential to help firms improve on productivity and bring down operating costs. Taken further, with ever-increasing socially and environmentally-conscious investors and the public alike, this act of natural resources management could have a significant implication on market value and income of the practicing firms.

The above proposition has been supported by sustainable business practices literature that is continuously conversing and deliberating upon the impact of efficient resource d

In light of accelerating environmental degradation, the transition to a green economy is an imperative for achieving sustainable development. This study provides a critical analysis of the international legal and institutional framework governing this transition, revealing a significant gap between normative developments and the institutional framework on one hand, and their practical implementation on the other. The transition faces legal obstacles, including reliance on non-binding voluntary commitments and conflicts between environmental obligations and global trade and investment rules. It also reveals a significant financing gap, as financial flows to developing countries continue to lag behind commitments, in add

There is no access to basic sanitation for half the world's population, leading to Socioeconomic issues, such as scarcity of drinking water and the spread of diseases. In this way, it is of vital importance to develop water management technologies relevant to the target population. In addition, in the separation form of water treatment, the compound often used as a coagulant in water treatment is aluminum sulfate, which provides good results for raw water turbidity and color removal. Studies show, however, that its deposition in the human body, even Alzheimer's disease, can cause serious harm to health and disease development. The study aims to improve the coagulation/flocculation stage related to the amount of flakes, i

     Credit card fraud has become an increasing problem due to the growing reliance on electronic payment systems and technological advances that have improved fraud techniques. Numerous financial institutions are looking for the best ways to leverage technological advancements to provide better services to their end users, and researchers used various protection methods to provide security and privacy for credit cards. Therefore, it is necessary to identify the challenges and the proposed solutions to address them.  This review provides an overview of the most recent research on the detection of fraudulent credit card transactions to protect those transactions from tampering or improper use, which includes imbalance classes, c

      The Mannich reaction is one of the most important types of organic chemistry fundamental reactions. It is a crucial stage in the production of various medicines, natural goods, and industrial chemicals. Chemists' imaginations have always been piqued because of this. In general, the Mannich reactions can be used as part of a tandem reaction sequence to produce complex target molecules in an elegant and often easy manner. The following article examines and summarizes methods for synthesizing Mannich derivatives, in addition to offering a survey of recent advancements in several fields’ applications of the Mannich reaction, such as biological applications, antimicrobial activity, anticancer activity, anti-inflammation and

MS Elias, RGM AL-helfy, Plant Archives, 2019